A Large Signal Theory or Traveling-Wave Amplifiers

The large-signal or nonlinear behavior of the traveling-wave amplifier is calculated in this paper by numerically integrating a set of equations of motion, which is essentially that of Nordsieck, but includes the space-charge repulsion between the electrons. The calculations were made assuming a loss-free circuit and a small coupling between the circuit and the beam. A method of computing the space-charge field, by summing the forces between the electrons, is fully described. It is found that in the large signal theory a parameter A is required in addition to the space-charge parameter QC. 1/k measures the range of action of the space-charge forces and is proportional to the beam radius. The other parameters including QC are those defined in the linear theory. Twenty cases covering useful ranges of the design and the operating parameters have been computed. The numerical integrations were done by type 701 IBM equipment. The amplitude and the phase of the circuit wave as functions of the distance are given for all the cases. It is found that the limiting efficiency increases with the electron injection speed, as found by Nordsieck, and increases with the space-charge parameter QC when QC is small, but decreases rapidly for larger QC. The efficiency also increases with the beam radius, or I/k, provided the assumption that the field and the current are uniformly distributed over the cross section is valid. Finally the electron motion in high level operation is analyzed. The effect of QC and of k on efficiency are explained.